Explain on what factors the ionization enthalpies of elements having $d^{\mathrm{n}}$ configuration depends upon ?

Explain the variation in ionization enthalpies of transition elements in $3 d$ series.

The ionization enthalpy depends on three factors.

$(i)$ Nucleus - electron attraction

$(ii)$ Electron - Electron repulsion

$(iii)$ Exchange energy

Exchange energy is responsible for the stabilization of the energy state. It is approximately proportional to the total numbers of possible pairs of parallel spin degenerate orbitals. When a several electrons occupy a set of degenerate orbitals, the lowest energy state corresponds to the maximum possible extent of single occupation of orbitals and parallel spins (Hund's Rule). The loss of exchange energy increases the stability and hence the ionization enthalpy increases.

$(i)$ First ionization enthalpy : The first ionization enthalpy follows a irregular trend. This is because, the first electron when removed alters the relative energies of $3 d$ and $4 s$ orbitals. The electrons are first removed from $4 s$ and then from $3 d$ orbitals.

In first transition series, going from scandium to zinc, the nuclear charge increases with the increase in atomic number and the electrons are added in $3 d$ orbitals. The increase in nuclear charge is opposed by the sheilding effect of $3 d$ electrons, as a result the atomic radii decreases less rapidly and so there is slight increase in ionization enthalpy in $3 d$ series.

$(ii)$ Successive ionization enthalpies: In general the third ionization enthalpy is higher than second ionization enthalpy which in turn is higher than first ionization enthalpy. The high values of successive ionization enthalpies is attributed to high effective nuclear charge and poor sheilding of one $d$-electron by other.

The second ionization enthalpy of chromium is higher than manganese while the third ionization enthalpy of manganese is higher than chromium. In case of chromium, the second electron is to be removed from half filled $\left(d^{5}\right)$ subshell which is extra stable and hence requires greater energy for ionization. In case of manganese, the third electron is to be removed from half filled $\left(d^{5}\right)$ subshell and so third ionization enthalpy is higher for manganese than chromium.

${ }_{24} \mathrm{Cr}^{+}:[\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{0} \rightarrow{ }_{24} \mathrm{Cr}^{2+}:[\mathrm{Ar}] 3 \mathrm{~d}^{4}$

${ }_{25} \mathrm{Mn}^{2+}:[\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{0} \rightarrow{ }_{25} \mathrm{Mn}^{3+}:[\mathrm{Ar}] 3 \mathrm{~d}^{4}$ (More difficult to attain)

Thus, for manganese, it is difficult to remove the third electron.

Similary, third ionization enthalpy of Mn is higher than Fe because Mn $^{2+}$ has $d^{5}$ configuration

while $\mathrm{Fe}^{2+}$ has $d^{6}$ configuration. So, the removal of electron from $\mathrm{Mn}^{2+}$ is difficult as the subshell

is half filled.

$\mathrm{Fe}^{2+}:\left[\begin{array}{ll}\text { Ar] } & 3 \mathrm{~d}^{6} 4 \mathrm{~s}^{0} \rightarrow \mathrm{Fe}^{3+}:\left[\text { Ar] } 3 \mathrm{~d}^{5}\right. \\ \mathrm{Mn}^{2+}: & {[\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{0} \rightarrow \mathrm{Mn}^{3+}:[\mathrm{Ar}] 3 \mathrm{~d}^{4}} \\ & \text { (More difficult to attain) } \\ \text { The first ionization enthalpy of Cu is less than zinc because the removal of } 4 \mathrm{~s} \text { electron in copper } \\ \text { will result in } \mathrm{d}^{10} \text { configuration (fully filled) while the second ionization of } \mathrm{Zn} \text { is lower than copper } \\ \text { as removal of second electron from zinc results in } \mathrm{d}^{10} \text { configuration (fully filled). } \\ { }_{29} \mathrm{Cu}:[\mathrm{Ar}] 3 \mathrm{~d}^{10} 4 \mathrm{~s}^{1} \rightarrow{ }_{29} \mathrm{Cu}^{+}:[\mathrm{Ar}] 3 \mathrm{~d}^{10} 4 \mathrm{~s}^{0} \\ {[\text { [Easy to attain] }} \\ { }_{30} \mathrm{Zn}^{+}:[\mathrm{Ar}] 3 \mathrm{~d}^{10} 4 \mathrm{~s}^{1} \rightarrow{ }_{30} \mathrm{Zn}^{2+}:[\mathrm{Ar}] 3 \mathrm{~d}^{10} 4 \mathrm{~s}^{0} \\ {[\text { [Easy to attain }]}\end{array}\right.$

$(iii)$ Stability of $\mathrm{M}^{2+}$ ions in gaseous state : The stability of $\mathrm{M}^{2+}$ ions in gaseous state depends on the summation of first and second ionization enthalpies and enthalpy of atomization. Lower is the sum of ionization enthalpy, greater is the thermodynamic stability. The dominant factor is second ionization enthalpy. This explains why the $\mathrm{Zn}^{2+}$ and $\mathrm{Mn}^{2+}$ ions are formed easily and removal of third electron is difficult. The high values of third ionization enthalpies of $\mathrm{Ni}, \mathrm{Cu}$ and $\mathrm{Zn}$ indicates why it is difficult to obtain oxidation states higher than two for these elements.